This is for a project I'm working on and it's just trying to figure out how many variations there are going to be, so I'll ask using a basic setup.
Ok, so the set up is this:
123
If we re-arrange the numbers without re-using any, we'll get 6 variations:
123
132
213
231
312
321
But then I change it to include a second line:
123
123
Now let's say we have the bottom line being the line that changes first so after 6 variations it'll end like so:
123
321
And then change the top, however, the bottom line does not go back to the first variation as the paring has already been used:
WRONG:
132
123
RIGHT:
132
132
Because of this rule (a name to this pattern would be useful please and thank you), instead of going through 6 variations until the top line changed again we only have 5, and each time we finish a cycle, we take one more out until we get to:
321
321
by which point we'd have had 21 variants. Meaning that 1=6, 2=21, 3=56.
My question is, what is the formula to work out this pattern?
